If the volume of a Box is 1,463,000 cubic millimetres, what is the volume of the box in cubic meters? (1 millimeter = 0.001 meter)

A) 14.63
B) 1.463
C) 0.1463
D) 0.01463
E) 0.001463

The trick here maybe to just drop the ugly numbers and transform 1,463,000 cubic mm into 1,000,000 cubic mm just to understand the logic behind.

If volume of a cube equals \(10^6\) cubic mm and the formula is side * side * side, we can infer that the side measures \(10^2\) mm, or 100 mm.

And 100 mm = 0.1 mt. Therefore the side measures 0.1 mt.

In volume, this would be represented as 0.1 mt * 0.1 mt * 0.1 mt, which yields 0.001 cubic mt.

The answer choice should have 2 zeroes between the point and the first decimal different to zero.
_________________

\(Well,\; square\; meters\; or\; cubic\; meters\; are\; simply\; m*m,\)

\(so\; our\; nice\; "a\; lot\; of\; millions"mm^{3},\; means\; x_{mm}\cdot y_{mm}\cdot z_{mm}\; and\; as\; each\; of\; these\; mm\; has\; a\; conversion\; of\; \frac{1}{1000},\)

\(the\; whole\; pack\; will\; need\; a\; reduction\; of\; 10^{-9}\; ,\; 9\; zeros,\; to\; become\; m^{3}.\)

\(Answer\; \mbox{E}.\)

\(Hope\; it\; helps.\;\) \(:)\)

Den

Hi pushpitkc

i dont get for some reason logic of sentence in red...

if 1 mm is 0.001 cubic mt. then

then shouldnt we divide 1463000 by 0,001

We know that when you multiply numbers with decimals, you multiply the numbers and then shift the decimal point to the left as many times as there are spaces to the right of the decimals in both numbers.

We are given that 1 millimeter = 0.001 meter

1 cubic meter= (.001)(.001)(.001) cubic millimeters

It follows that 1 cubic millimeter = 1 cubic meter (followed by 9 decimal shifts to the left).

How do we get from cubic millimeters to cubic meters? We shift the decimal 9 spaces to the left.

We can see that 7 shift gets us .1463000 so 9 shifts gets us .001463000 cubic meters